Poisson's ratio is defined as the ratio of lateral contraction to the longitudinal extension of a material subjected to tensile loading, and the ratio of lateral expansion to the longitudinal contraction in case of compressive loading. Most engineering materials possess positive Poisson's ratios in the vicinity of 0.3, and incompressible rubbery polymers exhibit a Poisson's ratio close to 0.5. The thermodynamic constraint of positive elastic moduli, i.e. positive shear and bulk moduli, restricts Poisson's ratio between −1 and 0.5. Though theoretically not forbidden, materials exhibiting negative Poisson's ratio are uncommon. Such materials are referred to as auxetics, a term coined by Professor Ken Evans of Exeter University, derived from the Greek word ‘auxesis,’ which means ‘increase’ or ‘grow.’
U.S. Pat. No. 4,668,557 to Lakes discloses a method of manufacturing auxetic open-cell foam based on a reentrant polyhedron structure as shown in FIGS. 1 and 2 of this application. The auxetic behavior of a-crystobalite, a SiO2 polymorph, has been demonstrated using Laser Brillouin spectroscopy. A few additional naturally occurring zeolites have been identified which exhibit auxetic nature, and others have theoretically predicted negative Poisson's ratio as a common feature of cubic metals, questioning the general belief of the rarity of naturally occurring auxetic materials. It has also been demonstrated by others that Poisson's ratio may not be bound between −1 and 0.5, a possibility characterized by the orthotropic constitutive equations and by positive definite energy density storage.
The physical explanation of the auxetic nature of the open-cell foam invented by Lakes, U.S. Pat. No. 4,668,557, is due to the unfolding lateral expansion of the strands of the reentrant polyhedron structure when subjected to tensile loads, involving three deformation mechanisms, namely, stretching, flexure, and hinging effects at the strand joints. On the other hand, the Possion's ratio has been experimentally determined to be as small as −0.8 for 3-dimensional reentrant foam structures, while approaching −1 by increasing volumetric compression ratio. The overall properties of the auxetic honeycomb structures are highly dependent on geometry, ranging from isotropic for regular hexagons to highly anisotropic, highly influenced by the variations in geometry. Numerical, analytical, and experimental procedures have proved that the mechanical properties of the conventional and reentrant honeycomb structures are highly dependent on relative density, which in turn is dependent upon the dimensions of the strands such as strand length, cross section, and angle. It has been reported that the Poisson's ratio becomes negative for a rib angle of 12.3° and a volume fraction of 0.1.
The present invention describes the design of a new class of auxetic structures termed as Rotational Expansion Novel Auxetic (RENA) structures. Auxetic materials of desired structural properties, i.e. stiffness and Poisson's ratios, can be tailor-made to an application at hand, using a wide variety of materials. Auxetic materials of various shapes and sizes, from nano-scale to mega-assemblies can be manufactured utilizing the developments in nanotechnology, manufacturing technologies, polymer chemistry, and structural engineering. Such tailor-made auxetic materials find applications in a wide variety of industries including biomedical and aerospace engineering.